Antennas

Rigorous Methods of Analysis and Synthesis

Boris Levin

• Publisher: CRC Press
• Year: 2021
• ISBN:
  9781000220056
• Edition: 1
• Topic: Informatik
• Subtopic: Computernetzwerke

The book comprises a new method of solving the integral equation of Leontovich, the most rigorous and most effective equation for the current in thin linear antennas. The book describes the features of the new method in its application in various types of antennas. It considers new ways of analyzing antennas, in particular in the calculation of an antenna gain based on main radiation patterns and the calculation of the directional characteristics of radiators with known distribution of current amplitude. The method of electrostatic analogy proposed by the author, provides the base for comparison of electromagnetic fields of high-frequency currents and electrostatic charges located on linear conductors to improve the directional characteristics of log-periodic and director-type antennas. A new approach to the analysis of the electrical characteristics of a microstrip antenna, which allows expansion of its operation range, is substantiated and developed. New results of antenna synthesis are obtained. The second part of the book is devoted to specific types of antennas (the author had a significant role in their creation). Particular attention is given to ship antennas for different frequency ranges.

The book is intended for professionals, working in electrodynamics and those working on development, placement and exploitation of antennas. It will be useful for lecturers (university-level professors), teachers, students of radio engineering and researchers working in various fields of radio electronics and interested in an in-depth study of theoretical problems and designs f antennas. It can also be used for short university courses.

Chapter 1
Straight Metal Radiator

The chapter of the book is devoted to the basic principles underlying the rigorous methods of analysis and synthesis of antennas. Among them, the method of integral equations for the current, which allows to calculate the current along antenna wires and determine all electrical characteristics of an antenna, starting with a simple linear radiator and moving on to complex one consisting of simple elements. For the analysis of a curvilinear radiator, the antenna is divided into simple rectilinear and curvilinear sections located along different coordinate axes. Points of the new sections must coincide with projections of points of the original antenna.

In accordance with the oscillating power theorem, the propagation of electromagnetic energy is understood as the transfer process of an energy transfer through the boundary of an enclosed space in which the source is located. The energy flow consists of two parts: active power, equal to the average value for the period of oscillation, and oscillating power varying with double frequency. Their values ​​are determined by the amplitudes and phases of the instantaneous values ​​of physical quantities included in the Maxwell equation.

The chapter successively examines well-known methods of antenna analysis, their advantages and disadvantages. For the physical interpretation of obtained results, the book uses the equivalent long line method, and the first chapter provides circuits of long lines for metal antennas with distributed and concentrated loads. The circuits are given, which were proposed for analyzing the mutual influence of horizontal systems of wires, parallel to the ground. Later they were used also for vertical wires.

1.1 Electromagnetic field

The simplest radiators are symmetric and asymmetric electric radiators of finite length (Fig. 1.1). A symmetrical radiator (dipole) is a straight-line conductor, whose currents at points symmetrical about its center are equal in magnitude and have the same direction. To create such a current distribution, an electromotive force (emf) source is included in the middle of the radiator, which divides it into two arms with the same length L (Fig. 1. 1a). An asymmetrical radiator is a straight conductor, excited by an emf source displaced from its middle (Fig. 1.1b). A special case of an asymmetric radiator is a monopole (Fig. 1.1c). This is a conductor with an emf at the base, mounted on a metal surface. The metal surface radiation replaces the radiation of the lower arm of the dipole. All these radiators are widely used in antenna technology. In addition, more complex antennas can be analyzed by breaking them into simple elements in the form of symmetrical or asymmetrical radiators. The significance of the theory of simple radiators is connected with this.

The modern theory of antennas is based on Maxwell’s equations—the basic equations of electrodynamics. The first two of them in the differential form appear as

(1.1)

where H^→ is a vector representing magnetic field strength, J^→ is a vector representing volume density of conduction current, D^→ is a vector representing electric displacement, t is time, E^→ is a vector representing electric field strength, B^→ is a vector representing magnetic induction. Hereinafter the International System of Units is used. The equations (1.1) are to be complemented with an equation of continuity

(1.2)

where ρ is a volume density of an electrical charge.

Typically, two more equations are included into a system of Maxwell’s equations:

(1.3)

but they follow from the equations (1.1) and (1.2) [1].

Fig 1.1. Symmetrical (a) and asymmetrical (b) metal radiators and monopole (c) from cylindrical wires.

The equations (1.1) interconnect the electromagnetic fields and currents in free space. It would be wrong to consider the left- or the right-hand side of an equation as the cause and, accordingly, the other side as the consequence. Both currents and electric and magnetic components of fields exist jointly only. None of the quantities are the prime cause of appearance of others. From (1.1) and (1.2) it follows for a harmonic field time-varying as exp(lωt) and an isotropic medium (D = εE...